EXTENSION OF THE RESIDUAL VARIABLE METHOD TO PROPAGATION PROBLEMS AND ITS APPLICATION TO THE WAVE-EQUATION IN CYLINDRICAL COORDINATES

1992-08-03
AKKAS, N
Tokdemir, Turgut
Consider a partial differential equation with cylindrical coordinates describing a dynamic process in an infinite medium with an inner cylindrical boundary. If an analytical solution to the problem is not possible, then one resorts to numerical techniques. In this case it becomes necessary to discretize the infinite domain even if the solution is required on the inner cylindrical surface or at a limited number of points in the domain only. The residual variable method (RVM) circumvents the difficulty associated with the discretization of the infinite domain. In essence, the governing equation is integrated once in a radial direction. The number of the spatial dimensions of the problem is reduced by one. It is now possible to determine the solution on the inner boundary without having to deal with the infinite domain. It is shown in this paper that the RVM is amenable to 'marching' solutions in a finite-difference implementation and that it is suitable for the analysis of propagation into the infinite medium from the inner surface. There is no need to discretize the infinite domain in its entirety at all. The propagation analysis can be terminated at any point in the radial direction without having to consider the rest.
COMPUTERS & STRUCTURES

Suggestions

The theorems of structural variation for rectangular finite elements for plate flexure
Saka, MP (Elsevier BV, 2005-11-01)
The theorems of structural variation predict the forces and displacements throughout a structure without the need of fresh analysis when the physical properties of one or more members are altered or even its topology is changed due to removal of one or more of its elements. It has been shown that a single linear elastic analysis of a parent structure under the applied loads and a set of unit-loading cases is sufficient to determine the elastic, non-linear elastic and even elasticplastic response of number o...
MODELING OF CONTROL FORCES FOR KINEMATICAL CONSTRAINTS IN MULTIBODY SYSTEMS DYNAMICS - A NEW APPROACH
IDER, SK (Elsevier BV, 1991-01-01)
Conventionally kinematical constrains in multibody systems are treated similar to geometrical constraints and are modeled by constraint reaction forces which are perpendicular to constraint surfaces. However, in reality, one may want to achieve the desired kinematical conditions by control forces having different directions in relation to the constraint surfaces. In this paper the conventional equations of motion for multibody systems, subject to kinematical constraints, are generalized by introducing gener...
ISOPARAMETRIC ELEMENTS WITH UNEQUALLY SPACED EDGE NODES
UTKU, M; CITIPITIOGLU, E; OZKAN, G (Elsevier BV, 1991-01-01)
In the isoparametric finite element formulation, mapping of equally spaced nodes on the boundary of the master element to unequally spaced locations on the physical elements results in an unacceptable distortion. This type of distortion is defined as 'node mapping distortion' and a technique for its elimination is presented. Simple test cases demonstrate the utility of the new formulation.
Extension of the residual variable method to propagation problems and its application to the diffusion equation in spherical coordinates
AKKAS, N; Tokdemir, Turgut (Springer Science and Business Media LLC, 1993-01-01)
We consider a partial differential equation in spherical (cylindrical) coordinates describing a dynamic process in an infinite medium with an inner spherical (cylindrical) boundary. If an analytical solution is not possible to obtain, then one resorts to numerical techniques. In this case it becomes necessary to discretize the infinite domain even if the solution is required on the inner spherical (cylindrical) surface or at a limited number of points in the domain only. The Residual Variable Method (RVM) c...
CHAOTIC DYNAMIC ANALYSIS OF VISCOELASTIC SHALLOW SPHERICAL-SHELLS
Karaesmen, Engin; ILERI, L; AKKAS, N (Elsevier BV, 1992-08-03)
This paper investigates the dynamic behaviour of a shallow, viscoelastic, spherical shell under a harmonic excitation. The time evolutions of the response of the corresponding nonlinear dynamical system are described by the phase portraits and the bifurcation of the parameter dependent system is studied numerically so as to identify qualitative changes in the phase portrait. The viscoelastic shell, having more than one equilibrium configuration for some problem parameters, shows periodic and/or random-like ...
Citation Formats
N. AKKAS and T. Tokdemir, “EXTENSION OF THE RESIDUAL VARIABLE METHOD TO PROPAGATION PROBLEMS AND ITS APPLICATION TO THE WAVE-EQUATION IN CYLINDRICAL COORDINATES,” COMPUTERS & STRUCTURES, pp. 729–734, 1992, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46231.